B Plane's Coanda's effect and jet engines sucking in air

I saw a video recently describing the lift in terms of pressure. It stated that the Coanda's effect is important. That is the tendency of a fluid jet to flow a curved path. It stated that there is high pressure above the top of an air foil and low pressure below so the air drops or gets sucked down like a vacuum. This easily describes the curving of air on the top of an air foil but not so easily for the bottom air flow which is also curved. The video also states that the curved streamlines have higher pressure outside than inside the line. Therefore, looking at the bottom it should have higher pressure. Although, the curvature shouldn't happen with this logic if the bottom surface of the air foil has higher pressure than below it. The logic of this video seemed to be off and I just want clarification.

Also, what about the front fan of a jet engine draws the air in? I think it has something to do with the origination of the air foils themselves but basically, what causes a fan to suck in or blow out? Thank you!

Whatever video you saw doesn't understand fluid mechanics, then. There are a number of issues with its description as you describe it here:

The Coandă effect has nothing to do with lift in general. Indeed, the Coandă effect has to do with a fluid jet following a surface, and there are no such jets over. for example, a wing.

If there was high pressure above the wing and low pressure below it, then you would have negative lift. The net force would be pushing down. Clearly this video is misunderstanding something.

There is no such concept of "inside" and "outside" a streamline. Streamlines are infinitesimally small. I suppose in this video maybe they mean that, for a curved streamline, the pressure is higher on the side of it nearer the center of curvature than the other side? If so, that is also incorrect. If you think about what is required to curve the path of something, you need a centripetal force of some kind, and in this case, that will correspond to a pressure gradient. In other words, the pressure is higher as you move further from the center of curvature.

With a typical jet engine, each individual fan blade is an airfoil. As the fan spins and move the airfoils through the air, it creates a low pressure region "above" each airfoil (i.e. on the side nearest the inlet), which will tend to be lower than the ambient pressure and draw air into the inlet. The work added by the engine serves to compress the air so that when it passes the airfoil it is now at a much higher pressure and can continue to expand through the engine (or go through multiple compression stages, as is the case on a modern jet engine). It's essentially the same way a propeller works, only the fan (and compressor stages) are contained and fuel is added to the air rather than a separate supply of air in a separate engine.

What causes the curvature of the air on both the top and bottom surfaces? I would expect the flow to continue in the same direction so straight line up (top surface) and down for bottom surface. Also, how does pressure get lower on top and higher on the bottom? I suspected the video to be wrong based on the explanation.